Calculating Test Statistic for Hypothesis Testing

In hypothesis testing, the test statistic helps us determine whether to reject the null hypothesis or not. The test statistic is often a standardized value that is calculated from sample data during a hypothesis test.

Suppose we are testing the null hypothesis $H_0: \mu = 100$ against the alternative hypothesis $H_1: \mu \neq 100$. In this context, the test statistic is calculated using the formula:

$$ z = \frac{\bar{x} - \mu_0}{\frac{\sigma}{\sqrt{n}}} $$

Where:

• $\bar{x}$ = sample mean
• $\mu_0$ = hypothesized mean (100 in this case)
• $\sigma$ = population standard deviation
• $n$ = sample size

If the sample mean $\bar{x}$ is 105, the population standard deviation $\sigma$ is 15, and the sample size $n$ is 30, what is the value of the test statistic?